Question 596732: Can someone please show me how to graph the equation y=1/2x^2+1 using symmetric properties?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The function  takes the same value for x as for -x.
Functions that do that are called even functions and are symmetrical with respect to the y-axis.
The y-axis is the line  .
You can get five points if you just calculate the value of the function at x=0, and at a couple of positive x values. You get the symmetrical points on the side with negative x for free.
For x=0,  , which gives you the point (0,1).
For x=2,  , which gives you the point (2,3).
For x=4,  , which gives you the point (4,9).
No calculations are required for the symmetrical points (-2,3) and (-4,9); you just change the sign of the x coordinate.
Next, plot the five points  and then draw a reasonable line
Doing it with pencil and paper, show my calculations first, with few, if any, words. Then I would have the line with the points clearly marked on just one graph, and I would include a table with the x and y values next to the graph. However, you should do it in whatever style your teacher prefers.
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